Moreover, it is investigated the finiteness conditions for capacities of some polyhedra by Kolodziejczyk (see [1]}, [2]}). For instance, a polyhedron \(Q\)  with finite fundamental group \(\pi _1 (Q)\) , and a polyhedron \(P\)  with abelian fundamental group \(\pi _1 (P)\)  and finitely generated homology groups \(H_i (\tilde{P})\) , for \(i\ge 2\) , have finite capacities (hence finite depths), where \(\tilde{P}\)  denotes the universal covering space of \(P\) .
